R9, N12NumberFoundation & HigherGrades 2–5

Percentages

"Per cent" means "out of 100", so 17% is $\frac{17}{100}$ or $0.17$ . Percentages are the most common real-world maths on GCSE papers: discounts, pay rises, interest, test scores and survey results. The key tool is the decimal multiplier, which turns every percentage question into a single multiplication.

40 min Video by Cognito AQA GCSE Maths

Before you start

Convert a percentage to a decimal and identify which quantity represents 100%.

Try this first. If you need the answer, revisit the prerequisite before continuing.

Starting check: A price falls by 15%. What percentage of the original price remains?

Show answer and reasoning

85%. The new price is 0.85 times the original.

The big picture

Without a calculator, build percentages from easy pieces: 10% is dividing by 10, 5% is half of that, 1% is dividing by 100. With a calculator, use the multiplier: 17% of £240 is $0.17 \times 240$ .

Increasing by 15% leaves you with 115% of the original, so multiply by $1.15$ . Decreasing by 15% leaves 85%, so multiply by $0.85$ . That one step replaces "find the percentage, then add or subtract", and it is essential for compound interest later.

GCSE Maths - Percentage Increase and Decrease (Multiplier Method) (2026/27 exams)Curated by Kepler, not produced by us. Watch it, then read the notes below.

Open on YouTube

Watch, pause, try

Video by Cognito. The video covers multiplier increases and decreases. Reverse percentages and successive changes are developed in the written practice.

Viewing focus: Translate a percentage change into the fraction of the original amount that remains.

After watching, attempt these questions before opening the answers. You can also use the written lesson below.

After watching 1: A £64 jacket is reduced by 25%. Find its sale price using one multiplication.

Show answer and reasoning

£64 × 0.75 = £48.

After watching 2: A £240 fee increases by 12%. Write the multiplier and find the new fee.

Show answer and reasoning

The multiplier is 1.12, so the new fee is £268.80.

KEPLER VISUAL LAB

Explore the idea

Predict what will change, then use the controls to test your explanation.

Increase, then decrease by10%

£100 × 1.1 × 0.9 = £99. The second change acts on a different amount, so equal percentage changes do not cancel.

On a narrow screen, scroll the diagram sideways to read every label.

What you'll learn

Find a percentage of an amount with and without a calculator
Write one quantity as a percentage of another
Increase and decrease by a percentage using multipliers
Calculate simple interest and compare offers

Percentage of an amount

Non-calculator: find 10% (divide by 10), 5% (half of 10%) and 1% (divide by 100), then add pieces. For 35%: $10\% \times 3 + 5\%$ .

Calculator: convert the percentage to a decimal and multiply. $12.5\%$ of 64 is $0.125 \times 64 = 8$ .

Example 1Without a calculator, find 35% of £260.

110% = £26, so 30% = £78.

25% = £13.

335% = £78 + £13.

Answer

£91

Your turnSame method, new numbers — try it before moving on.

Without a calculator, find 15% of £340.

Your answer

Show worked solution

Solution

110% = £34 and 5% = £17.
215% = £34 + £17 = £51.

Answer: £51

Example 2Find 17.5% of £84.

17.5\% = 0.175

0.175 \times 84 = 14.7

Answer

£14.70

Your turnSame method, new numbers — try it before moving on.

Find 8% of 2,350 kg.

Your answer

Show worked solution

Solution

1 $0.08 \times 2350 = 188$ kg.

Answer: $188$ kg

Tip — Money answers need 2 decimal places: £14.70, not £14.7.

One quantity as a percentage of another

Write the part as a fraction of the whole, then multiply by 100. Make sure both are in the same units first.

Example 1Sam scored 42 out of 56 in a test. What percentage is this?

\frac{42}{56} \times 100

= 0.75 \times 100 = 75\%

Answer

75\%

Your turnSame method, new numbers — try it before moving on.

What is 45 cm as a percentage of 3 m?

Your answer

Show hint

Change 3 m to centimetres first.

Show worked solution

Solution

1 $3$ m $= 300$ cm.
2 $\frac{45}{300} \times 100 = 15\%$ .

Answer: $15\%$

Percentage increase and decrease

The multiplier for an increase of $p\%$ is $1 + \frac{p}{100}$ ; for a decrease it is $1 - \frac{p}{100}$ .

Increase 80 by 12%: $80 \times 1.12 = 89.6$ . Decrease 80 by 12%: $80 \times 0.88 = 70.4$ .

An increase of 15% leaves 115% of the original; a decrease of 15% leaves 85%.

Example 1A £450 laptop is reduced by 22% in a sale. Find the sale price.

1Multiplier:

1 - 0.22 = 0.78

450 \times 0.78 = 351

Answer

£351

Your turnSame method, new numbers — try it before moving on.

A salary of £28,500 increases by 3.5%. What is the new salary, in pounds?

Your answer

Show worked solution

Solution

1Multiplier: $1.035$ .
2 $28500 \times 1.035 = 29497.5$ , so £29,497.50.

Answer: £29,497.50

Why the order of changes matters

Increasing by 20% and then decreasing by 20% does not get you back to the start: $100 \times 1.2 \times 0.8 = 96$ . The decrease is 20% of a bigger number. Multipliers make this obvious.

Simple interest and best buys

Simple interest pays the same amount every year: interest = principal × rate × years. £2000 at 3% for 4 years earns $2000 \times 0.03 \times 4 = £240$ .

To compare offers, work out the final price or value for each and state which is better with the figures.

Example 1Shop A: coat £80, 25% off. Shop B: same coat £75, 1/5 off. Which is cheaper?

1A:

80 \times 0.75 = £60

2B:

\frac{1}{5}

of 75 is 15, so £60.

Answer

They cost the same — £60.

Your turnSame method, new numbers — try it before moving on.

£1,800 is invested at 2.5% simple interest per year. How much interest is earned in 6 years, in pounds?

Your answer

Show worked solution

Solution

1Interest per year: $1800 \times 0.025 = £45$ .
2Over 6 years: $6 \times 45 = £270$ .

Answer: £270

Think like an examiner

In "which is the better buy" questions, the final mark needs a conclusion supported by figures for both options.
Write the multiplier you use ( $0.78$ , $1.035$ ) — it earns the method mark even if you mistype into the calculator.
Give money to 2 decimal places and include units.

Percentages

p\% \text{ of } A = \frac{p}{100} \times A

Percentage of an amount.

\frac{\text{part}}{\text{whole}} \times 100

One quantity as a percentage of another.

A \times \left(1 \pm \frac{p}{100}\right)

Increase or decrease by

p\%

Watch out for these

Using

1.5

as the multiplier for a 5% increase.

5% increase is

1.05

Decreasing by 22% using

0.22

That finds the discount. The sale price uses

0.78

45 cm as a percentage of 3 m:

\frac{45}{3} \times 100

Same units:

\frac{45}{300} \times 100 = 15\%

Thinking +20% then −20% returns to the original.

1.2 \times 0.8 = 0.96

— a 4% overall loss.

Stretch yourself

In a sale, prices are reduced by 30%. On the last day, the sale prices are reduced by a further 30%. Is this the same as a 60% reduction? If not, what is the overall percentage reduction?

Hint — Apply both multipliers to a starting price of £100.

Reveal solution

Solution

100 \times 0.7 \times 0.7 = 49

, so the final price is 49% of the original — a 51% reduction, not 60%. The second 30% is taken off an already-reduced price.

\blacksquare

Questions students ask

How do I find 1% without a calculator?

Divide by 100. Then any whole percentage is a multiple of 1%, e.g. 7% is

7 \times 1\%

Can a percentage be more than 100?

Yes. A price rising from £20 to £50 is 250% of the original. You cannot, however, take away more than 100% of something.

What is the difference between simple and compound interest?

Simple interest is calculated on the original amount each year. Compound interest is calculated on the growing total — see Percentage Change & Growth.

Key takeaways

Non-calculator: build from 10%, 5% and 1%.
Calculator: multiply by the decimal equivalent.
Part as a percentage: $\frac{\text{part}}{\text{whole}} \times 100$ , same units.
Increase by $p\%$ : × $(1 + \frac{p}{100})$ ; decrease: × $(1 - \frac{p}{100})$ .
Simple interest = principal × rate × years.

Exam-style questions

Practise it the way it is examined

3 original questions · 11 marks, written to match the style and mark allocation of the real papers. Work on paper, then open the mark scheme and tick the marks you earned — method marks count even if the final answer slips.

Question 1Grade 22 marks

Work out 45% of 620 without a calculator.[2]
Show mark scheme
- M1A correct build-up, e.g. $10\% = 62$ and $5\% = 31$
- A1 $279$
Answer: $279$

Question 2Grade 45 marks

Priya earns £2,150 a month. She spends £731 on rent.

(a)What percentage of her monthly pay does she spend on rent?[2]
Show mark scheme (a)
- M1 $\frac{731}{2150} \times 100$
- A1 $34\%$
Answer: $34\%$
(b)Her pay rises by 4%. Her rent rises by 6%. What percentage of her new pay is her new rent? Give your answer to 1 decimal place.[3]
Show mark scheme (b)
- M1New pay $2150 \times 1.04 = 2236$ or new rent $731 \times 1.06 = 774.86$
- M1 $\frac{774.86}{2236} \times 100$
- A1 $34.7\%$
Answer: $34.7\%$

Question 3Grade 54 marks

Two phone contracts run for 24 months. Contract A: £180 up front, then £26 per month. Contract B: no up-front cost, £38 per month, with 15% off the total.

Which contract is cheaper overall, and by how much?[4]
Show mark scheme
- M1Total for A: $180 + 24 \times 26 = £804$
- M1Total for B: $24 \times 38 \times 0.85$
- A1B $= £775.20$
- A1B is cheaper by £28.80
Answer: B, by £28.80

Unlimited practice

Skill drill

A new question every time, marked instantly, with a full worked solution. Aim for a streak of five, then move up a level.

0 / 0 first-time correct Streak 0Best at this level: 0

Generating a question…

Complete the method

Some of the setup is done. Finish it on paper, then compare your reasoning.

Your turn: After a 20% discount, a bag costs £56. Complete: original × ___ = 56; original = ___.

Show a hint

The sale price represents 80%, not 100%.

Show answer and reasoning

Original × 0.8 = 56, so original = 56 ÷ 0.8 = £70. Check: 20% of £70 is £14.

Spot and repair the mistake

Identify the first incorrect step and explain how to fix it.

Diagnose it: A student says a 10% increase followed by a 10% decrease returns £100 to £100. Test the claim.

Show answer and reasoning

The price becomes £110, then £110 × 0.9 = £99. The decrease uses the larger base of £110. The combined multiplier is 1.1 × 0.9 = 0.99.

Apply it in an exam

Write a full response before revealing the solution. These are Kepler-authored exam-style questions; the suggested marks are a self-check guide.

Question 1 · 4 marks: Shop A reduces a £90 item by 30%. Shop B reduces the same starting price by 20%, then takes another 10% off its reduced price. Which is cheaper and by how much?

Show answer and reasoning

A costs £90 × 0.7 = £63. B costs £90 × 0.8 × 0.9 = £64.80. A is cheaper by £1.80.

Calculate the first final price as £63.
Use successive multipliers for B.
Calculate B as £64.80.
Compare final prices: A by £1.80.

Explore further

AQA 8300 specification (opens in a new tab)
Check the assessed content, tier requirements and official course documents.
Corbettmaths: percentages practice (opens in a new tab)
Further percentage practice. Choose questions appropriate to your tier.

Recall and check later

Return with the notes closed. Answer from memory, check the reasoning, then practise anything you missed.

Recall 1: Tomorrow: after a 5% rise, a membership costs £126. Find its previous price.

Show answer and reasoning

£126 ÷ 1.05 = £120.

Recall 2: In a week: a price falls from £80 to £68. What is the percentage decrease?

Show answer and reasoning

The decrease is £12. Divide by the original £80, then multiply by 100: 15%.

Test yourself

Answer a few questions, then review anything you missed.

Prefer paper? Open the written self-check

Answer each question before opening its answer. This self-check does not record a quiz score.

What is 10% of 90?
- $9$
- $0.9$
- $10$
- $81$
Show answer and explanation
Answer: $9$
Divide by 10.
What is 25% of £48?
- £12
- £24
- £25
- £4.80
Show answer and explanation
Answer: £12
25% is a quarter.
Write 18 out of 40 as a percentage.
- $45\%$
- $18\%$
- $22\%$
- $40\%$
Show answer and explanation
Answer: $45\%$
$\frac{18}{40} = 0.45$ .
What is the multiplier for a 7% decrease?
- $0.93$
- $0.07$
- $1.07$
- $0.7$
Show answer and explanation
Answer: $0.93$
$100\% - 7\% = 93\%$ .
Increase £65 by 20%.
- £78
- £85
- £13
- £52
Show answer and explanation
Answer: £78
$65 \times 1.2$ .
Simple interest on £500 at 4% for 3 years is…
- £60
- £20
- £562.43
- £560
Show answer and explanation
Answer: £60
$500 \times 0.04 \times 3$ .
A price rises by 10% then falls by 10%. The overall change is…
- a 1% decrease
- no change
- a 1% increase
- a 20% decrease
Show answer and explanation
Answer: a 1% decrease
$1.1 \times 0.9 = 0.99$ .
What is 0.5% of 3,000?
- $15$
- $150$
- $1.5$
- $1500$
Show answer and explanation
Answer: $15$
1% is 30, so 0.5% is 15.

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